Three-mode Cepheid pulsation

Amplitude equations, that are used in the investigation of stellar pulsations, for the three-mode nonresonant coupling case are inferred from that of the two-mode nonresonant coupling case. Characteristics of the fixed points of the amplitude equations are studied. Chaotic behaviour is expected when the amplitude equations consist of more than two modes.     

Long-term waves on Cepheid pulsation period trends

The secular evolution of the pulsation period of δ Cephei, η Aquilae, and ζ Geminorum during a cumulative total of 577 years suggests wave-like departures about the smooth time trends.     

Linear nonadiabatic pulsation models of the double-mode Cepheid V371 Per

A recently found double-mode Cepheid with the shortest known period in our Galaxy and abnormal period ratio,V371 Per,is investigated by linear nonadiabatic pulsation models.V371 Per is likely to be crossing the instability strip for the first time,because the mass derived from pulsation models is larger than the evolution mass for the second or higher crossing objects.This result seems to support the conclusion obtained from spectroscopic observation.We also found that models with observed period and period ratio of V371 Per need to have mass and T_(eff) in a narrow range which shifts as heavy element abundance Z changes.We have checked the agreement between T_(eff) ranges estimated observationally and derived from pulsation models using observational Z.We found that those ranges overlap marginally.We need more spectroscopic estimations of T_(eff) and [Fe/H],and more photometric monitoring to estimate the evolutional period change for confirmation of our result.     

Period-doubling as a limit to pulsation of short-period population II Cepheid models

The short-period limiting pulsation found by Fadeyev and Fokin (1985) in a short-period, Population II Cepheid model is examined by means of the Baker-von Sengbush-Stellingwerf (BSS) algorithm of limit cycles.It is shown that the model has a stable limit cycle of the fundamental mode and an unstable limit cycle of the first overtone mode. When the method is applied for pulsations spanning the time interval of twice the period of the fundamental mode, we find only the fundamental cycle repeated doubly or the first overtone limit cycle repeated three times, depending on initial conditions of the integration.We thus conclude that the period-doubling limiting pulsation found by Fadeyev and Fokin (1985) is a transient feature of the model.     

Extragalactic Cepheid database

We present in this paper an exhaustive compilation of all published data of extragalactic Cepheids. We have checked every light curve in order to characterize the different types of Cepheid and detect potential overtone pulsators, or to estimate the quality of the data. This compilation of about 3000 photometric measurements will constitute a very useful tool for astronomers involved for instance in the extragalactic distance scale.     

Nonlinear astrophysical dynamo: Three-mode interaction

The effect of mode-coupling on the temporal variation of the linearly unstable magnetic mode is investigated for weakly unstable dynamos. It is shown that the nonlinear coupling of the unstable mode to itself is the dominant effect which stabilizes the mode at a certain amplitude rather than the coupling to other damped modes.     

Period changes of Cepheid variables

Secular period changes of one hundred northern Cepheids are investigated with the help of O–C diagrams. With the classical Cepheids the rate of observed period changes is in good agreement with that determined from stellar evolution theory. The period noise cannot mask the evolutionary period changes especially in longer period Cepheids for which the occurrence of parabolic O–C graphs is unusually frequent.     

Cepheid parallaxes and the Hubble constant

Revised Hipparcos parallaxes for classical Cepheids are analysed together with 10 Hubble Space Telescope ( HST )-based parallaxes. In a reddening-free V , I relation we find that the coefficient of log  P is the same within the uncertainties in our Galaxy as in the Large Magellanic Cloud (LMC), contrary to some previous suggestions. Cepheids in the inner region of NGC 4258 with near solar metallicities confirm this result. We obtain a zero-point for the reddening-free relation and apply it to the Cepheids in galaxies used by Sandage et al. to calibrate the absolute magnitudes of Type Ia supernova (SNIa) and to derive the Hubble constant. We revise their result for H ₀ from 62 to 70 ± 5 km s⁻¹ Mpc⁻¹. The Freedman et al. value is revised from 72 to 76 ± 8 km s⁻¹ Mpc⁻¹. These results are insensitive to Cepheid metallicity corrections. The Cepheids in the inner region of NGC 4258 yield a modulus of 29.22 ± 0.03 (int.) compared with a maser-based modulus of 29.29 ± 0.15. Distance moduli for the LMC, uncorrected for any metallicity effects, are 18.52 ± 0.03 from a reddening-free relation in V , I ; 18.47 ± 0.03 from a period–luminosity relation at K ; 18.45 ± 0.04 from a period–luminosity–colour relation in J , K . Adopting a metallicity correction in V , I from Macri et al. leads to a true LMC modulus of 18.39 ± 0.05.     

Cepheid kinematics and the Galactic warp

The space velocities of 200 long-period (P>5 days) classical Cepheids with known proper motions and line-of-sight velocities whose distances were estimated from the period-luminosity relation have been analyzed. The linear Ogorodnikov-Milne model has been applied, with the Galactic rotation having been excluded from the observed velocities in advance. Two significant gradients have been found in the Cepheid velocities, ?W/?Y = ?2.1 ± 0.7 km s^?1 kpc^?1 and ?V/?Z = 27 ± 10 km s^?1 kpc^?1. In such a case, the angular velocity of solid-body rotation around the Galactic X axis directed to the Galactic center is ?15 ± 5 km s^?1 kpc^?1.     

The eight-schwabe-cycle pulsation

The shape of the Sun’s secular activity cycle is found to be a saw-tooth curve. The additional Schwabe cycle 4′ (1793–1799) suggested by Usoskin, Mursula, and Kovaltsov (2001a) is taken into account in the telescopic sunspot record (1610–2001). Instead of a symmetrical Gleissberg cycle, a saw-tooth of exactly eight Schwabe sunspot maxima (‘Pulsation’) is found. On average, the last sunspot maximum of an eight-Schwabe-cycle saw-tooth pulsation has been about three times as high as its first maximum. The Maunder Minimum remains an exception to this pattern. The Pulsation is defined as a secular-scale envelope of Schwabe-cycle maxima, whereas the Gleissberg cycle is a result of long-term smoothing of the sunspot series.     

The eight-schwabe-cycle pulsation

The shape of the Sun’s secular activity cycle is found to be a saw-tooth curve. The additional Schwabe cycle 4′ (1793–1799) suggested by Usoskin, Mursula, and Kovaltsov (2001a) is taken into account in the telescopic sunspot record (1610–2001). Instead of a symmetrical Gleissberg cycle, a saw-tooth of exactly eight Schwabe sunspot maxima (‘Pulsation’) is found. On average, the last sunspot maximum of an eight-Schwabe-cycle saw-tooth pulsation has been about three times as high as its first maximum. The Maunder Minimum remains an exception to this pattern. The Pulsation is defined as a secular-scale envelope of Schwabe-cycle maxima, whereas the Gleissberg cycle is a result of long-term smoothing of the sunspot series.     

Double-mode stellar pulsation

The current observational and theoretical status of the double-mode variables is reviewed. Focusing mostly on the RR Lyrae stars, we address the question of the observational evidence ofmodal stability. The problem of stationarity is a crucial issue in the modelling of these stars.We mention past efforts in hydrodynamical and analytical modelling together with a detailed discussion of some very recent results. It is suggested that stochastic forcing due to turbulent convection may play a crucial role in exciting some marginally stable modes in the limiting pulsation. The latest hydrodynamical results first demonstrate that purelyradiative models are able to showpermanent double-mode behavior in the relevant period regime of RRd stars. The reason for the previous lack of double-mode behavior is attributed to the large dissipation,i.e. artificial viscosity, generally used in the codes to ensure numerical stability and to obtain amplitudes comparable to the observed ones.We think that better models should include some physical dissipation, most probably turbulent convection, and a more accurate numerical treatment of the radiative hydrodynamics.     

Cepheid Limb Darkening Models for the VLTI

We present a new method to compute wavelength- and phase-dependent limb darkening corrections for classical Cepheids. These corrections are derived from hydrodynamic simulations and radiative transfer modeling with a full set of atomic and molecular opacities. Comparison with hydrostatic models having the same stellar parameters show a larger limb darkening for most phases in our models, and temporal variations related to the hydrodynamics of the stellar pulsation. Weassess the implications of our results with respect to the geometric Baade-Wesselink method, which uses interferometric measurements of Cepheid angular diameters to determine their distances and radii. The relevance of the hydrodynamic effects predicted by our model on the limb darkening of pulsating Cepheids is finally discussed in terms of the predicted capabilities of the VLTI. This revised version was published online in July 2006 with corrections to the Cover Date.     

A new Cepheid variable,HD 200925

Photoelectric observations of the star HD 200925 in the standardUBV system have been secured and analysed. The period is determined to be 0 _. ^d 267 394. From the period and shape of the light and colour curves, the star HD 200925 appears to be a dwarf cepheid. The physical parameters have been derived. The mass derived for this star is found to agree well with the value inferred from the evolutionary tracks. The star appears to be a post-Main Sequence star in the hydrogen shell burning stage of evolution. The spectral class, for this star, is assigned to be F2 III.     

Patterns of aperiodic pulsation

Techniques for deriving amplitude equations for stellar pulsation are outlined. For the simplest such equations with multiple instabilities, the derivation of a map for the patterns of pulsation phases is described. This map gives the time between two successive maxima of pulsation in terms of the time between the previous pair, under suitable conditions. The phase differences can be regular, chaotic or hyperchaotic.     

Determination of Cepheid parameters by light-curve template fitting

We describe techniques to characterize the light curves of regular variable stars by applying principal component analysis (PCA) to a training set of high-quality data, and to fit the resulting light-curve templates to sparse and noisy photometry to obtain parameters such as periods, mean magnitudes etc. The PCA approach allows us to efficiently represent the multiband light-curve shapes (LCSs) of each variable, and hence quantitatively describe the average behaviour of the sample as a smoothly varying function of period, and also the range of variation around this average.
In this paper we focus particularly on the utility of such methods for analysing Hubble Space Telescope ( HST ) Cepheid photometry, and present simulations which illustrate the advantages of our PCA template-fitting approach. These are: accurate parameter determination, including LCS information; simultaneous fitting to multiple passbands; quantitative error analysis; objective rejection of variables with non-Cepheid-like light curves or those with potential period aliases.
We also use PCA to confirm that Cepheid LCSs are systematically different (at the same period) between the Milky Way and the Large and Small Magellanic Clouds, and consider whether LCS might therefore be used to estimate the mean metallicities of Cepheid samples, thus allowing metallicity corrections to be applied to derived distance estimates.     

Spectroscopic studies of the small-amplitude Cepheid SU Cas

A new set of 16 high-resolution spectra for the small-amplitude Cepheid SU Cas obtained in 2007–2009 has allowed us to determine its atmospheric parameters (T _eff = 6345 ± 30 K, log g = 2.40, V _t = 3.25 km s^?1) and to measure its radial velocities. The latter were added to the general list of radial velocities (375 estimates) obtained in the last 90 years. Using a frequency analysis, we have refined the pulsation and orbital periods of the Cepheid. Apart from the well-known fundamental pulsation period , we have detected a possible secondary period of . Their ratio of 0.96 suggests the existence of nonradial pulsations in the Cepheid’s atmosphere. Based on photoelectric photometry in the last 60 years, we have shown that the effective temperature undergoes cyclic secular changes of ±200 K with an unknown period. The mean effective temperature T _eff = 6395 ± 52 K estimated from photometric data agrees well with our estimate from spectroscopic data. The variations of the mean color index, effective temperature, and γ-velocity (in 90 years of observations) point to a possible orbital motion of the well-known hot companion with the most probable periods of , , and . The elemental abundances in the atmosphere of SU Cas confirm the conclusion that this Cepheid is a typical yellow supergiant after the first dredge-up. Our T _eff estimate gives a radius of 32R _⊙ and a distance of 455 pc for it, which is inconsistent with its membership in the open cluster Alessi 95. The question about the pulsation mode of SU Cas still remains open.     

The spectroscopic period of the Cepheid SU Cassiopeiae

The spectroscopic period of the short periodic Cepheid SU Cas was determined from the radial velocity measurements by ABT, GIEREN and HÄUPL. The calculated period is 1.949312 days. Radial velocity differences between measurements by GIEREN and HÄUPL are explained as velocity zero point of the used spectrographs. The zero point of the Tautenburg Coudé spectrograph was determined by measuring the radial velocity standard star ϵ Leo. The difference to the standard value was -0.7 km/s. No significant differences are found between the spectroscopic period and light curve of SU Cas in the last 35 years.     

V473 Lyrae: a Blazhko-effect Cepheid?

The amplitude spectra of the light curves of RR Lyrae Blazhko stars can often be typified by symmetrical triplets. It is shown that the same applies to V473 Lyr. Furthermore, the star is probably a radial pulsator – as is thought to be the case for the RR Lyrae stars – thus ruling out rotational splitting of a purely non-radial mode.